• Help seekers: Roughly 19 percent of parents are most concerned with finding out their own children’s academic progress and learning how they can help their students improve. . . . The majority say they don’t know how and don’t have time to do more than they already are doing to be involved in school.

• School helpers: This 27 percent of parents is the closest to the traditional picture of the “PTA mom and dad.” Nearly three out of four of them have already volunteered at the school in the past year, and they are most likely of all parents to trust the school officials. According to the study, these parents are open to “traditional” school involvement such as hall monitoring or fundraising, but less comfortable with contributing to school policies.

• Potential transformers: Finally, 31 percent of parents said they were interested in and ready to be more involved in shaping how the schools operate. They are more likely to be aware of how their own school and district stack up to others in terms of academic performance and teacher qualifications, and they are also more likely than other parents to know what classes and skills their children need to be prepared for college. However, only between a quarter and a third of these parents have actually been asked to get more involved.

Half of Kansas City parents said they could be more involved at their child’s school if they made an effort.

The struggle for P.S. 84 will determine whether Latino immigrant parents can share a Brooklyn school with middle-class whites who are gentrifying the Williamsburg neighborhood.

The first round of integration went badly, reports Capital New York. In fall of 2006, P.S. 84 was “83 percent Latino, but the 8 percent of white students comprised nearly half of the Pre-K and Kindergarten classes.” The “newcomer” parents were eager to volunteer in classrooms, contribute their fund-raising skills and lead the PTA.

. . . during elections for the School Leadership Team, a council that comprises parents and staff. (Brooke) Parker, the Pre-K parent, stood up to give her stump speech. Depending on whom you ask, the speech was either a galvanizing call to improve the school or an affront to its teachers and pre-existing parents. Also depending on whom you ask, Parker was rudely heckled or duly called out for her own rudeness.

“I was heckled by the faculty, in front of my kids,” Parker complains. “The faculty was like, ‘Who are you to come in here?’ The insinuation was that I couldn’t be accountable to anyone except my constituency, which was perceived to be middle-class.”

Jaime Estades, who later became PTA president, put it another way: “A parent stood up and talked about how bad the teaching in the school was and that changes had to be made. You can’t just say that to a bunch of teachers.”

Newcomer parents objected to the school’s annual Three Kings Day parade, a cultural tradition for Latino parents. Newcomers objected to selling ice cream in Pre-K classes to help fund the PTA. Newcomers, many of them involved in the arts, wanted progressive education, while immigrant parents favored traditional methods.

The reception they received shocked the newcomer parents. As they saw it, they were working hard to turn a bad school into a good one only to run into opponents who kept making it about race.

Few white students went on to first grade at P.S. 84, which went through several principals before hiring a Latina raised in Williamsburg.

Sereida Rodriguez-Guerra is trying to lure new students. She’s introduced progressive educational programs, such as “the Renzulli method, which matches curriculum to students’ learning styles and interests, as well as the Visual Thinking Strategies program, which aims to improve critical thinking and descriptive language skills through discussion of visual images.”

Test scores remain low — the school has an “F” rating — which advocates blame on previous administrations. The principal says the school doesn’t “teach to the test.”

The atmosphere is calmer, though tensions remain between parent groups. “Last year, a group of mostly newcomer parents volunteered their time, money and artisanal skills to renovate the long-defunct library.” Other newcomers are redesigning the school’s web site.

White enrollment is back up to 7.6 percent, mostly in pre-K and kindergarten. But middle-class white families won’t stick with P.S. 84 without signs of academic progress.

If the school remains half-empty, the unused space is likely to be given to a charter school. P.S. 84 loyalists say that will destroy their school.